XRF Tomography — X-ray Fluorescence CT L1-134
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.
Forward model E
A pencil or focused X-ray beam (synchrotron or microfocus source) excites K/L fluorescence of elements; fluorescent photons emitted isotropically are collected via energy-dispersive detector. Pencil-beam raster + rotation yields projections of elemental concentration; CT inversion reconstructs 3D elemental maps at ~1-10 um resolution.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- unique at full-angle, low-Z, thin samples; thick high-Z samples suffer self-absorption nonlinearity
- Stability:
- conditional
- κ:
- 500
Linear at low concentration; self-absorption breaks linearity (must be corrected iteratively). Limited-angle geometry adds ill-posedness.
Solvability C
- Solver class:
- FBP-with-attenuation, iterative SART with self-absorption correction, ML-EM, learned XRF-Net
- Convergence rate q:
- 2
- Complexity:
- FBP O(N^2 log); iterative O(iter * N_view * N_voxel)